On a roll is a slangy expression that has been used since around the 1970s, especially to describe being on a ‘winning streak.’ It seems to alludes to the idea that an object that is rolling will continue to roll because of its momentum. Thus, if someone is on a roll, not only are they now enjoying success but will continue to for some period of time.
The word roll itself has been used in this way since the 1800s. Therefore, it is unlikely that this idiom derived from the national lottery, based on the practice of ‘rolling’ the winning amount forward if nobody won the previous lottery, as some sources claim, is unlikely. Another claim is that it comes from gambling, where a person rolling the dice and winning will continue to roll the dice.
To be “on something” in this instance means to be engaged in something. If roll alludes to a series of successes, then “on a roll” means to be engaged in a series of successes.
In another idiom, roll means a way of behaving, as in the way I roll. It is also used in the sexual idiom a roll in the hay, alluding to how people engaged in sexual intercourse might ‘roll around’ on a bed (where hay equals bed).
Other idioms using the word roll:
rolled into one: combined into one; possessing multiple characteristics (alluding to two or more things being “rolled” into a bundle.
ready to roll: prepared to begin something; ready to leave (alluding to wheels rolling on a vehicle; ready to start filming (alluding to film rolling).
roll up one’s sleeves: to get ready for hard work (based on literally rolling up one’s sleeves to prepare for hard work, presumably to keep one’s sleeves clean or prevent them from getting in the way).
More Idiom Origins (Etymology)